Given the first inequality,
[tex]5x-2<13[/tex]Let us solve for x,
[tex]\begin{gathered} \text{collect like terms,} \\ 5x<13+2 \\ 5x<15 \\ \text{divide both sides by 5} \\ \frac{5x}{5}<\frac{15}{5} \\ x<3 \end{gathered}[/tex]Given the second inequality,
[tex]\begin{gathered} -6x+2>-28 \\ \text{collect like terms,} \\ -6x>0-28-2 \end{gathered}[/tex][tex]\begin{gathered} -6x>-30 \\ \text{divide both sides -6} \\ \frac{-6x}{-6}<\frac{-30}{-6} \\ x<5 \end{gathered}[/tex]The solutions for x for the two inequalities are,
[tex]\begin{gathered} x<3,\text{ and} \\ x<5 \end{gathered}[/tex]Hence, we have
[tex](-\infty,3)\cap(-\infty,5)=(-\infty,3)[/tex]Hence, the solution is the interval (-∞, 3)
